1. Technical Field
The present invention relates to a method for manufacturing a resonator element, a wafer, a resonator element, a resonator, an oscillator, a real-time clock, an electronic apparatus, and a moving object.
2. Related Art
Electronic devices such as a resonator or an oscillator have been widely used in a small information apparatus such as a HDD (hard disk drive), a mobile computer, or an IC card, or a mobile communication apparatus such as a mobile phone, a car phone, or a paging system.
A resonator element used in the electronic device includes a base portion and a pair of vibrating arms extending from the base portion. The resonator element is obtained by, for example, etching a wafer made of quartz crystal or the like to form an outer shape in which a portion of the base portion is connected to a base material via a break-off portion (coupling portion) and then cutting the break-off portion.
For example, JP-A-2003-198303 discloses a resonator element in which a break-off portion is provided at an edge of a base portion on the side opposite to vibrating arms. Moreover, JP-A-2008-177723 discloses a resonator element in which a break-off portion is provided at both edges of a base portion in a direction in which a pair of vibrating arms are arranged side by side.
In the resonator element disclosed in JP-A-2003-198303, however, when the length of the base portion is shortened for miniaturizing the resonator element with recent demands for miniaturization, stress may be concentrated, in break-off, on the vicinity of a side surface of the base portion on the vibrating arm side. Hence, it may be impossible to achieve miniaturization.
Moreover, in the resonator element disclosed in JP-A-2008-177723, the break-off portion is provided at both edges of the base portion in the direction in which the pair of vibrating arms are arranged side by side. Therefore, compared with the case where the break-off portion is provided at one edge, a resonance frequency F1′ of a spurious mode (a flexural vibration mode in which the pair of vibrating arms repeatedly make a flexural motion in the same direction in a plan view) in a wafer state may be remarkably higher than a resonance frequency F1 in a singulated state after break-off from the wafer, due to the fact that the resonator element is firmly fixed to the wafer via the break-off portions (coupling portions).
In contrast, in a main mode (a flexural vibration mode in which the pair of vibrating arms alternately separate from and approach each other repeatedly in the plan view), since the main motion of the flexural vibration of the pair of vibrating arms is a flexural motion in which the pair of vibrating arms are deformed in opposite directions in the plan view, most of motions are canceled out around the base portion, and thus the main mode is less likely to be affected by the break-off portion. Therefore, the resonance frequency F0′ in the wafer state is rarely different remarkably from the resonance frequency F0 in the singulated state after break-off from the wafer due to whether the break-off portion is provided at both edges or one edge of the base portion in the direction in which the pair of vibrating arms are arranged side by side (except the difference due to the coupling of the main mode and the spurious mode).
Hence, in the resonator element disclosed in JP-A-2008-177723, if a resonance frequency change due to the coupling of the main mode and the spurious mode is excluded, there is the case where, due to the fact that the difference |F0′−F1′| between the resonance frequency F0′ of the main mode and the resonance frequency F1′ of the spurious mode measured in the wafer state is remarkably smaller than the difference |F0−F1| between the resonance frequency F0 of the main mode and the resonance frequency F1 of the spurious mode measured in the singulated state after break-off from the wafer, the coupling of the main mode and the spurious mode in the wafer state is remarkably stronger than the coupling of the modes in the singulated state after break-off. The resonance frequency F0′ of the main mode in the wafer state is changed by the influence of this coupling.
A change in the strength of this coupling depends on variations in the shape dimensions of the resonator element or break-off portion. Therefore, the difference between F0′ and F0 greatly varies according to manufacturing variations in forming the shape of the resonator element or break-off portion. As a result, it is difficult to precisely estimate the resonance frequency F0 after break-off from the resonance frequency F0′ in the wafer state. Therefore, accuracy in adjusting the frequency of the main mode in the wafer state is deteriorated, which may lower the yield.